Fill in the blanks:
(i) (………) `+(-5/6)=-30`
(ii) (………….) `+(-8) = (-3/4)`
(iii) `(-15/14) + (…………) = 5/2`
(iv) `(-16) + (………..) = 6`

Answer

Let's solve each part step by step.

### (i) Fill in the blank: \( (………) + (-\frac{5}{6}) = -30 \)

1. Let the blank be represented by \( x \). So we have:
\[ x + (-\frac{5}{6}) = -30 \]
2. To isolate \( x \), we can add \( \frac{5}{6} \) to both sides:
\[ x = -30 + \frac{5}{6} \]
3. To perform this addition, we need a common denominator. The common denominator of 1 and 6 is 6. We can rewrite -30 as:
\[ -30 = -\frac{180}{6} \]
4. Now, we can add:
\[ x = -\frac{180}{6} + \frac{5}{6} = -\frac{180 - 5}{6} = -\frac{175}{6} \]

**Final answer for (i)**: \( -\frac{175}{6} \)

### (ii) Fill in the blank: \( (………….) + (-8) = -\frac{3}{4} \)

1. Let the blank be \( x \):
\[ x + (-8) = -\frac{3}{4} \]
2. To isolate \( x \), we can add 8 to both sides:
\[ x = -\frac{3}{4} + 8 \]
3. Rewrite 8 with a common denominator of 4:
\[ 8 = \frac{32}{4} \]
4. Now, we can add:
\[ x = -\frac{3}{4} + \frac{32}{4} = \frac{32 - 3}{4} = \frac{29}{4} \]

**Final answer for (ii)**: \( \frac{29}{4} \)

### (iii) Fill in the blank: \( (-\frac{15}{14}) + (…………) = \frac{5}{2} \)

1. Let the blank be \( x \):
\[ -\frac{15}{14} + x = \frac{5}{2} \]
2. To isolate \( x \), we can add \( \frac{15}{14} \) to both sides:
\[ x = \frac{5}{2} + \frac{15}{14} \]
3. We need a common denominator to add these fractions. The common denominator of 2 and 14 is 14. Rewrite \( \frac{5}{2} \):
\[ \frac{5}{2} = \frac{35}{14} \]
4. Now, we can add:
\[ x = \frac{35}{14} + \frac{15}{14} = \frac{35 + 15}{14} = \frac{50}{14} \]
5. Simplify \( \frac{50}{14} \):
\[ x = \frac{25}{7} \]

**Final answer for (iii)**: \( \frac{25}{7} \)

### (iv) Fill in the blank: \( (-16) + (………..) = 6 \)

1. Let the blank be \( x \):
\[ -16 + x = 6 \]
2. To isolate \( x \), we can add 16 to both sides:
\[ x = 6 + 16 \]
3. Perform the addition:
\[ x = 22 \]

**Final answer for (iv)**: \( 22 \)

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